• 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

Operation on rational numbers

This topic has 4 expert replies and 2 member replies

Operation on rational numbers

Post
An OG question

Q. At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day
crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the
two crews did the day crew load?

(A) 1/2
(B) 2/5
(C) 3/5
(D) 4/5
(E) 5/8

Don't really follow the explanation given in the OG.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
Quote:
At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?

(A) 1/2

(B) 2/5

(C) 3/5

(D) 4/5

(E) 5/8
Day crew:
Let the number of workers = 5.
Let the number of boxes loaded by each worker = 4.
Total number of boxes loaded = 5*4 = 20.

Night crew:
Since the night crew has 4/5 as many workers as the day crew, the number of workers on the night crew = (4/5)5 = 4.
Since each worker on the night crew loads 3/4 as many boxes as each worker on the day crew, the number of boxes loaded by each night crew worker = (3/4)4 = 3.
Total number of boxes loaded = 4*3 = 12.

(Boxes loaded by the day crew)/(Total number of boxes loaded by the two crews) = 20/(20+12) = 20/32 = 5/8.

The correct answer is E.

_________________
Mitch Hunt
Private Tutor for the GMAT and GRE
GMATGuruNY@gmail.com

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.
Student Review #1
Student Review #2
Student Review #3

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

GMAT/MBA Expert

Post
HI saadishah,

TESTing VALUES (the approach that Mitch used) is a fairly easy way to work through this question. If you want to use an Algebraic approach, then that's fine, but you have to be very careful about what your variables represent.

The number of night workers is related to the number of day workers...

IF...
N = number of night workers
D = number of day workers

N = (4/5)D

Next, you have to create a variable and an equation for the number of boxes loaded per employee.

B = number loaded per day worker
(3/4)B = number loaded per night worker

Now we can set up a ratio of boxes loaded by the Day workers to TOTAL boxes loaded by all workers:

(D)(B) / [ (D)(B) + (N)(3/4)(B) ]

Since N = (4/5)D, we can substitute in that value...

DB / [DB + (4/5)(D)(3/4)(B)]

Next, we can multiply and simplify...

DB / [DB + (12/20)DB]
DB / (32/20)DB]
1 / [32/20]

20/32 = 5/8

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
Quote:
At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?


A. 1/2
B. 2/5
C. 3/5
D. 4/5
E. 5/8

I think the fast way is to plug in some nice numbers.
Since the two pieces of information regarding the night shift are related to the information regarding the day shift, let's assign some nice values to the DAY shift.

Number of workers

Day shift: 5 workers (this is an easy number to find 4/5 of)
Night shift: 4 workers (4/5 of 5 = 4)

Boxes loaded per worker
Day shift: 4 boxes per worker
Night shift: 3 boxes per worker (3/4 of 4 = 3)

Total boxes loaded
Day shift: 5 workers times 4 boxes per worker = 20 boxes
Night shift: 4 workers times 3 boxes per worker = 12 boxes

Combined total boxes for both shifts = 20 + 12 = 32

Of the 32 boxes, the day shift loaded 20 of them.
20/32 = 5/8

Answer: E

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Sign up for our free Question of the Day emails
And check out all of our free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
Newbie | Next Rank: 10 Posts Default Avatar
Joined
12 Jan 2016
Posted:
2 messages
Post
saadishah wrote:
An OG question

Q. At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day
crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the
two crews did the day crew load?

(A) 1/2
(B) 2/5
(C) 3/5
(D) 4/5
(E) 5/8

Don't really follow the explanation given in the OG.
As given in the problem night crew loaded 3/4 boxes and there are 4/5 workers as compared to day crew, so in effect their work is 3/4 * 4/5= 3/5 times the day crew's work, which means the ratio of night crew's work to day crew's work is 3:5. That easily gives the fraction of work by day crew, i.e 5/(3+5) = 5/8.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
saadishah wrote:
An OG question

Q. At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day
crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the
two crews did the day crew load?

(A) 1/2
(B) 2/5
(C) 3/5
(D) 4/5
(E) 5/8
We are given that the night crew loaded 3/4 as many boxes as each worker on the day crew and that the night crew has 4/5 as many workers as the day crew.

4/5 x (number of day workers) = number of night workers

Let's choose the convenient value of 20 for the number of day workers and substitute it into the equation above:

4/5 x 20 = number of night workers

16 = number of night workers

Next, we set up the equation for the number of boxes loaded by each worker.

3/4 x (number of boxes loaded by each day worker) = number of boxes loaded by each night worker

Now let's choose the convenient value of 8 for the number of boxes loaded by each day worker and substitute it into the above equation:

3/4 x 8 = number of boxes loaded by each night worker

6 = number of boxes loaded by each night worker

Thus, the total number of boxes loaded by each type of worker is as follows:

Day workers = 20 x 8 = 160

Night workers = 16 x 6 = 96

Total boxes loaded = 160 + 96 = 256

The question asks us to determine the fraction of all the boxes loaded by the day crew, and that is:

(Total boxes loaded by day crew)/(Total boxes loaded)

160/256 = 40/64 = 5/8

Answer: E

_________________
Jeffrey Miller Head of GMAT Instruction

  • +1 Upvote Post
  • Quote
  • Flag
Newbie | Next Rank: 10 Posts Default Avatar
Joined
24 Sep 2018
Posted:
3 messages
Post
Day workers (20)
Night workers (20) * (4/5) = 16

Number of boxes per day worker = 1 per worker so (20 ) total
Number of boxes per night worker = (3/4)*(16) = 12 total for night worker

combined day and night = 20 + 12 = 32
Day / combined = 20/32, simplified, divided the top and bottom by (4)

Number of Workers for day
20/32 divided by 4/4 = 5/8

  • +1 Upvote Post
  • Quote
  • Flag
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep

Top First Responders*

1 fskilnik@GMATH 90 first replies
2 Brent@GMATPrepNow 48 first replies
3 Jay@ManhattanReview 43 first replies
4 Rich.C@EMPOWERgma... 26 first replies
5 GMATGuruNY 26 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description fskilnik@GMATH

GMATH Teacher

171 posts
2 image description Scott@TargetTestPrep

Target Test Prep

118 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

100 posts
4 image description Max@Math Revolution

Math Revolution

83 posts
5 image description Jay@ManhattanReview

Manhattan Review

71 posts
See More Top Beat The GMAT Experts